Skip to main content
SpringerLink
Log in

Study on centrality measures in social networks: a survey

  • Review Article
  • Published:
Social Network Analysis and Mining Aims and scope Submit manuscript

Abstract

Social networks are absolutely a useful and important place for connecting people within the world. A basic issue in a social network is to identify the key persons within it. This is why different centrality measures have been found over the years. In this survey paper, we present past and present research works on measures of centrality in social network. For this plan, we discuss mathematical definitions and different developed centrality measures. We also present some applications of centrality measures in biology, research, security, traffic, transportation, drug, class room. At last, our future research work on centrality measure is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Bae J, Kim S (2014) Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Phys A 395:549–559

    Article  MathSciNet  MATH  Google Scholar 

  • Barrat A et al (2004) The architecture of complex weighted networks. Proc Natl Acad Sci 101(11):3747–3752

    Article  Google Scholar 

  • Bavelas A (1948) A mathematical model for group structures. Appl Anthropol 7:16–30

    Google Scholar 

  • Bavelas A (1950) Communication patterns in task oriented groups. J Acoust Soc Am 22:725–730

    Article  Google Scholar 

  • Beauchamp MA (1965) An improved index of centrality. Behav Sci 10:161–163

    Article  Google Scholar 

  • Boccaletti S et al (2006) Complex networks: structure and dynamics. Phys Rep 424:175–308

    Article  MathSciNet  MATH  Google Scholar 

  • Bonacich P (1972) Factoring and weighing approaches to status scores and clique identification. J Math Sociol 2(1):113–120

    Article  Google Scholar 

  • Bonacich P (1987) Power and centrality: a family of measures. Am J Sociol 92(5):1170–1182

    Article  Google Scholar 

  • Bonacich P (2007) Some unique properties of eigenvector centrality. Soc Netw 29:555–564

    Article  Google Scholar 

  • Bonacich P, Lloyd P (2001) Eigenvector-like measures of centrality for asymmetric relations. Soc Netw 23(3):191–201

    Article  Google Scholar 

  • Borgatti SP (2006) Identifying sets of key players in a social network. Comput Math Organ Theory 12:21–34

    Article  MATH  Google Scholar 

  • Borgatti SP et al (2009) Network analysis in the social sciences. Sci New Ser 323(5916):892–895

    Google Scholar 

  • Brandes U (2001) A faster algorithm for betweenness centrality. J Math Sociol 25(2):163–177

    Article  MATH  Google Scholar 

  • Brandes U (2008) On variants of shortest-path betweenness centrality and their generic computation. Soc Netw 302:136–145

    Article  Google Scholar 

  • Bruun J, Brewe E (2013) Talking and learning physics: predicting future grades from network measures and Force Concept Inventory pretest scores. Phys Rev Phys Educ Res 9:020109

    Article  Google Scholar 

  • Chen CM (2006) Cite space II: detecting and visualizing emerging trends and transient patterns in scientific literature. J Am Soc Inform Sci Technol 57(3):359377

    Article  Google Scholar 

  • Coles N (2001) Analyzing serious crime groups as social network. Br J Criminol 41:580–594

    Article  Google Scholar 

  • Costenbader E, Valente TW (2003) The stability of centrality measures when networks are sampled. Soc Netw 25:283–307

    Article  Google Scholar 

  • Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271

    Article  MathSciNet  MATH  Google Scholar 

  • Estrada E, Rodriguez-Velazquez JA (2005) Subgraph centrality in complex networks. Phys Rev 71:056103

    MathSciNet  Google Scholar 

  • Everett MG, Borgatti SP (1999) The centrality of groups and classes. J Math Sociol 23(3):181–201

    Article  MATH  Google Scholar 

  • Fletcher JM, Wennekers T (2017) From structure to activity: using centrality measures to predict neuronal activity. Int J Neural Syst 27:1750013

    Google Scholar 

  • Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41

    Article  Google Scholar 

  • Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1:215–239

    Article  Google Scholar 

  • Freeman LC, Borgatti SP, White DR (1991) Centrality in valued graphs: a measure of betweenness based on network flow. Soc Netw 13(2):141–154

    Article  MathSciNet  Google Scholar 

  • Garas A, Schweitzer F, Havlin S (2012) A k-shell decomposition method for weighted networks. New J Phys 14:083030

    Article  Google Scholar 

  • Grunspan DZ, Wiggins BL, Goodreau SM (2014) Understanding classrooms through social network analysis: a primer for social network analysis in education research. CBE Life Sci Educ 13:167–178

    Article  Google Scholar 

  • Guimera R et al (2005) The worldwide air transportation network: anomalous centrality, community structure, and cities global roles. Proc Natl Acad Sci 102(22):7794–7799

    Article  MathSciNet  MATH  Google Scholar 

  • Hage P, Harary F (1995) Eccentricity and centrality in networks. Soc Netw 17:57–63

    Article  Google Scholar 

  • Holme P (2003) Congestion and centrality in traffic flow on complex networks. Adv Complex Syst 6(2):163–176

    Article  MATH  Google Scholar 

  • Jayaweera IMLN, Perera KKKR, Munasinghe J (2017) Centrality measures to identify traffic congestion on road networks: a case study of Sri Lanka. IOSR J Math 13(2):13–19

    Article  Google Scholar 

  • Jeong H et al (2001) Lethality and centrality in protein networks. Nature 411(6833):41–42

    Article  Google Scholar 

  • Joyce KE et al (2010) A new measure of centrality for brain networks. PLoS ONE 5(8):12200

    Article  Google Scholar 

  • Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43

    Article  MathSciNet  MATH  Google Scholar 

  • Kitsak M et al (2010) Identification of influential spreaders in complex networks. Nat Phys 6(11):888–893

    Article  Google Scholar 

  • Koschutzki D et al. (2005) Centrality indices. In: Brandes U, Erlebach T (eds.) Network analysis: methodological foundations 3418:16–61

  • Koschutzki D, Schreiber F (2008) Centrality analysis methods for biological networks and their application to gene regulatory networks. Gene Regul Syst Biol 2:193–201

    Google Scholar 

  • Koschützki D, Schreiber F (2004) Comparison of centralities for biological networks. German Conf Bioinf 53:199–206

    Google Scholar 

  • Liu X et al (2005) Co-authorship networks in the digital library research community. Inf Process Manage 41:1462–1480

    Article  Google Scholar 

  • Liu LG et al (2007) Weighted network properties of Chinese nature science basic research. Phys A Stat Mech Appl 377(1):302–314

    Article  Google Scholar 

  • Liu JG, Ren ZM, Guo Q (2014) Ranking the spreading influence in complex networks. Phys A 392(18):4154–4159

    Article  Google Scholar 

  • Liu Y et al (2015) Identify influential spreaders in complex networks: the role of neighborhood. Phys A 452:289–298

    Article  Google Scholar 

  • Newman MEJ (2001) Scientific collaboration networks I. Network construction and fundamental results. Phys Rev E 64:016131

    Article  Google Scholar 

  • Newman MEJ (2004) Analysis of weighted networks. Phys Rev E 389:2134–2142

    Google Scholar 

  • Newman MEJ (2010) Networks: an introduction. Oxford University Press, New York

    Book  MATH  Google Scholar 

  • Nieminen J (1974) On the centrality in a graph. Scand J Psychol 15:322–336

    Article  Google Scholar 

  • Opsahl T, Panzarasa P (2009) Clustering in weighted networks. Soc Netw 31:155–163

    Article  Google Scholar 

  • Opsahl T, Agneessens F, Skvoretz J (2010) Node centrality in weighted networks. Generalizing degree and shortest paths. Soc Netw 32(3):245–251

    Article  Google Scholar 

  • Rhemtulla M et al (2016) Network analysis of substance abuse and dependence symptoms. Drug Alcohol Depend 161:230–237

    Article  Google Scholar 

  • Rodriguez JA, Estrada E, Gutierrez A (2006) Functional centrality in graphs. Linear Multilinear Algebra 55:293–302

    Article  MathSciNet  MATH  Google Scholar 

  • Sabidussi G (1966) The centrality index of a graph. Psychometrika 31(4):581–603

    Article  MathSciNet  MATH  Google Scholar 

  • Shaw ME (1954) Group structure and the behavior of individuals in small groups. J Psychol 38:139–149

    Article  Google Scholar 

  • Shimbel A (1953) Structural parameters of communication networks. Bull Math Biophys 15(4):501–507

    Article  MathSciNet  Google Scholar 

  • Sparrow MK (1991) The application of network analysis to criminal intelligence: an assessment of the prospects. Soc Netw 13(3):251–274

    Article  Google Scholar 

  • Stephenson K, Zelen M (1989) Rethinking centrality: methods and examples. Soc Netw 11:1–37

    Article  MathSciNet  Google Scholar 

  • Tew KL, Li XL, Tan SH (2007) Functional centrality: detecting lethality of proteins in protein interaction networks. Genome Inform 19:166–177

    Google Scholar 

  • Wang K and Xiufen F (2017) Research on centrality of urban transport network nodes, AIP Conference Proceedings 1839, 020181

  • Wang J et al (2017) A novel weight neighborhood centrality algorithm for identifying influential spreaders in complex networks. Phys A S0378–4371(17):30121–30128

    Google Scholar 

  • White DR, Borgatti SP (1994) Betweenness centrality measures for directed graphs. Soc Netw 16:335–346

    Article  Google Scholar 

  • Wuchty S, Stadler PF (2003) Centers of complex networks. J Theor Biol 223(1):45–53

    Article  MathSciNet  Google Scholar 

  • Yan E, Ding Y (2009) Applying centrality measures to impact analysis: a co-authorship network analysis. J Am Soc Inform Sci Technol 60(10):2107–2118

    Article  Google Scholar 

  • Zeng A, Zhang CJ (2013) Ranking spreaders by decomposing complex networks. Phys Lett A 377(14):1031–1035

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Kousik Das & Madhumangal Pal

  2. Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, 721636, India

    Sovan Samanta

Authors
  1. Kousik Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sovan Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sovan Samanta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, K., Samanta, S. & Pal, M. Study on centrality measures in social networks: a survey. Soc. Netw. Anal. Min. 8, 13 (2018). https://doi.org/10.1007/s13278-018-0493-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13278-018-0493-2

Keywords

Search

Navigation